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A Mixture Model for Survival Data with Both Latent and Non-Latent Cure Fractions

Author

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  • Eduardo Yoshio Nakano

    (Department of Statistics, University of Brasilia, Campus Darcy Ribeiro, Asa Norte, Brasilia 70910-900, Brazil)

  • Frederico Machado Almeida

    (Department of Statistics, University of Brasilia, Campus Darcy Ribeiro, Asa Norte, Brasilia 70910-900, Brazil)

  • Marcílio Ramos Pereira Cardial

    (Institute of Mathematics and Statistics, Federal University of Goias, Goiania 74001-970, Brazil)

Abstract

One of the most popular cure rate models in the literature is the Berkson and Gage mixture model. A characteristic of this model is that it considers the cure to be a latent event. However, there are situations in which the cure is well known, and this information must be considered in the analysis. In this context, this paper proposes a mixture model that accommodates both latent and non-latent cure fractions. More specifically, the proposal is to extend the Berkson and Gage mixture model to include the knowledge of the cure. A simulation study was conducted to investigate the asymptotic properties of maximum likelihood estimators. Finally, the proposed model is illustrated through an application to credit risk modeling.

Suggested Citation

  • Eduardo Yoshio Nakano & Frederico Machado Almeida & Marcílio Ramos Pereira Cardial, 2025. "A Mixture Model for Survival Data with Both Latent and Non-Latent Cure Fractions," Stats, MDPI, vol. 8(3), pages 1-15, September.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:3:p:82-:d:1748916
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    References listed on IDEAS

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    1. Yolanda M. Gómez & Diego I. Gallardo & Marcelo Bourguignon & Eduardo Bertolli & Vinicius F. Calsavara, 2023. "A general class of promotion time cure rate models with a new biological interpretation," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 66-86, January.
    2. Lore Dirick & Gerda Claeskens & Bart Baesens, 2017. "Time to default in credit scoring using survival analysis: a benchmark study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(6), pages 652-665, June.
    3. Rodrigues, Josemar & Cancho, Vicente G. & de Castro, Mrio & Louzada-Neto, Francisco, 2009. "On the unification of long-term survival models," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 753-759, March.
    4. Martin G. Larson & Gregg E. Dinse, 1985. "A Mixture Model for the Regression Analysis of Competing Risks Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(3), pages 201-211, November.
    5. Vicente G. Cancho & Gladys Barriga & Jeremias Leão & Helton Saulo, 2021. "Survival model induced by discrete frailty for modeling of lifetime data with long-term survivors and change-point," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(5), pages 1161-1172, March.
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